I have following two questions:

1.Consider a bond that promises to pay coupons annually for 10 years. The face value is $1000. The riskfree rate is 2% (annually). The bond, however, is not risk free: the entity that issues the bond may default. If the entity defaults during the period (t,t+1], that means that the payments scheduled at the beginning of year 1,...,t were paid, but the payments scheduled on year t+1,..., T will not be paid. Suppose that the probability of default during period (t,t+1], given that there was no default during [0,t], is 0.05, for t=0,1,...,T-1.

a) Suppose that the coupon rate is set to 3%. When they are detached from the bond, coupon payments are reinvested at the risk-free rate.

(i) Compute, for each year, the probability that the payment scheduled for year t is paid.

(ii) Deduce the expectation of the nominal value of the payment of year t for all t.

(iii) Compute the value of the bond on year 0, assuming a discount rate equal to the risk-free rate. b) Suppose now that the coupon rate should be set such that the price of the risky bond on year 0 is equal to its face value, $1000, taking into account the 0.05 default probability during each period. Compute the coupon rate, assuming the discount rate used to value payments is equal to the risk-free rate.

b) Suppose now that the coupon rate should be set such that the price of the risky bond on year 0 is equal to its face value, $1000, taking into account the 0.05 default probability during each period. Compute the coupon rate, assuming the discount rate used to value payments is equal to the risk-free rate.

2.Consider a bond that promises to pay coupons annually for 10 years. The face value is $1000. The riskfree rate is 2%. The coupon rate is 3%. The bond is currently trading at $463. Assuming that payments are deposited at the risk-free rate, compute the default probability p that the bond defaults during a period (t, t+1] given that there was no default during [0,t]; do this in the case where a) the recovery rate is 0%: if the bond defaults, all future scheduled payments cease to exist. b) the recovery rate is 20%: if the bond defaults, a terminal payment equivalent to 20% of the face value is made at the time of default (and all future scheduled payments cease to exist).

Here is the pics of there two questions. Thanks!

Consider a bond that promises to pay coupons annually for 10 years. The face value is $1000. The risk- free rate is 2% (annually). The bond, however, is not risk free: the entity that issues the bond may default. If the entity defaults during the period (t,t+1], that means that the payments scheduled at the beginning of year t were paid, but the payments scheduled on year t+1,..., T will not be paid Suppose that the probability of default during period (t,t+1], given that there was no default during [0,t, is 0.05, for T-1 a) Suppose that the coupon rate is set to 3%. When they are detached from the bond, coupon payments are reinvested at the risk-free rate. (i) Compute, for each year, the probability that the payment scheduled for year t is paid. (ii) Deduce the expectation of the nominal value of the payment of year t for all t. (iii) Compute the value of the bond on year 0, assuming a discount rate equal to the risk-free rate. b) Suppose now that the coupon rate should be set such that the price of the risky bond on year 0 is equal to its face value, $1000, taking into account the 0.05 default probability during each period. Compute the coupon rate, assuming the discount rate used to value payments is equal to the risk-free rate. Consider a bond that promises to pay coupons annually for 10 years. The face value is $1000. The risk- free rate is 2% (annually). The bond, however, is not risk free: the entity that issues the bond may default. If the entity defaults during the period (t,t+1], that means that the payments scheduled at the beginning of year t were paid, but the payments scheduled on year t+1,..., T will not be paid Suppose that the probability of default during period (t,t+1], given that there was no default during [0,t, is 0.05, for T-1 a) Suppose that the coupon rate is set to 3%. When they are detached from the bond, coupon payments are reinvested at the risk-free rate. (i) Compute, for each year, the probability that the payment scheduled for year t is paid. (ii) Deduce the expectation of the nominal value of the payment of year t for all t. (iii) Compute the value of the bond on year 0, assuming a discount rate equal to the risk-free rate. b) Suppose now that the coupon rate should be set such that the price of the risky bond on year 0 is equal to its face value, $1000, taking into account the 0.05 default probability during each period. Compute the coupon rate, assuming the discount rate used to value payments is equal to the risk-free rate